How do I find the domain of f(x, y) =4-x^2-2y^2

Question

anonymous · Answer

$$\large f(x, y) =4-x^{2}-2y^{2} $$

anonymous · Answer

i know how to do it when there are fractions and the denominator cannot equal 0 or the natural logarithm of something most be greater than zero but dont have any restrictions on this one so not sure what to do. @hartnn

anonymous · Answer

Perhaps the simplest way is to consider a 2D section (contour map).

So u set f(x,y) = constant c  (if c is 0 y have an ellipse, then vary c up and down, see what happens)

hartnn · Answer

i would say since  x is not restriced because of any square root sign or denominator, the domain is all real numbers.....

hartnn · Answer

*restricted

zarkon · Answer

this is a polynomial.  the domain for a polynomial is not restricted.  Therefore the domain is $\mathbb{R}\times\mathbb{R}$